-2/y-3=-1/2y-6-1

Solution for -2/y-3=-1/2y-6-1 equation:

-2/y-3=-1/2y-6-1

We move all terms to the left:

-2/y-3-(-1/2y-6-1)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y-6-1)!=0

We move all terms containing y to the left, all other terms to the right

2y-1)!=6

y∈R


We add all the numbers together, and all the variables

-2/y-(-1/2y-7)-3=0

We get rid of parentheses

-2/y+1/2y+7-3=0

We calculate fractions


(-4y)/2y^2+y/2y^2+7-3=0

We add all the numbers together, and all the variables

(-4y)/2y^2+y/2y^2+4=0

We multiply all the terms by the denominator


(-4y)+y+4*2y^2=0

We add all the numbers together, and all the variables

y+(-4y)+4*2y^2=0

Wy multiply elements

8y^2+y+(-4y)=0

We get rid of parentheses

8y^2+y-4y=0

We add all the numbers together, and all the variables

8y^2-3y=0

a = 8; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·8·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*8}=\frac{0}{16}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*8}=\frac{6}{16}
=3/8
$